Hence, for \(c_{s*} \ll 1\)  we have that the spectral tilt will turn
blue, i.e., \(n_s-1>0\) , if \(\beta > 1.7\) , while for \(c_{s*}=1\) , the
spectral tilt is blue for \(\beta > 1.5\) . We recall that for this
case [1]} we have that \(\beta \simeq 2.315\)  (for
\(c_{s*}=1\) ), thus, for large \(Q\)  this dissipation coefficient with a
quartic inflaton potential will always be in disagreement with the
observations. But from Eq. (REF ), we expect that
\(\beta \)  will decrease proportional to \(c_s^2\) . Thus, we need at least
\(c_{s*}^2 \lesssim 1.7/2.315 \sim 0.7\)  for the model to be able to
sustain a large dissipation DBIWI regime and to have a red tilted
scalar of curvature power spectrum, consistent with the
observations. This expectation will be confirmed by our numerical
results shown in Sec. .
